The underside of an overhanging cornice of a building extending out from the plane of the building walls.
Merriam-Webster Online Dictionary
soffit (noun) the underside of a part or member of a building (as of an overhang or staircase) , especially the intrados of an arch
soffit (Wikipedia)
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Eaves or soffit lining on a house in Northern Australia. The flat section (underside) would be referred to as a soffit. In this example the soffit is fixed to the slope of the rafters. The fascias form the outer edge and have a groove in them to receive the soffit lining sheets.
A soffit is an exterior or interior architectural feature, generally the underside of any construction element. A structure to fill the space between the ceiling and the top of cabinets mounted on the wall is called a soffit, as is the material connecting an exterior wall to the edge of the roof under the eaves.